JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Heat & Thermodynamics

The root mean square velocity of molecules of gas is

(A)Proportional to square of temperature $(T^{2})$ .
(B)Inversely proportional to square root of temperature $\frac{1}{T}$ .
(C)Proportional to square root of temperature $T$ .✓ Correct
(D)Proportional to temperature (T).

Answer: (C)

Solution

The root-mean-square speed follows from

\frac{1}{2} m ⟨ v^{2} ⟩ = \frac{3}{2} k T

, which gives

v_{rms} = \frac{3 R T}{M}

. With

R

and

M

fixed this leaves

v_{rms} \propto T

. The root-mean-square velocity is proportional to the square root of the absolute temperature.

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option

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